1. The points P(1,4,5) and Q(3,2,1) are determined by the stationary vectors and .

2. The vector and the normal vector of the given plane span the new plane. Additionally the new plane has to pass through P (or Q).

3. The normal vector of the new plane is

4. yields the equation of the new plane.

EDIT: I've attached the graphs of the 2 planes. The Points P and Q are drawn in blue and red respectively.